The perception that life on other planets would be, problematic for religious people, and indeed for religion itself, is a longstanding one. It is partially rooted in fact: astrobiological speculations have, on occasion, engendered religious controversies. Historical discussions are often far more nuanced, and less one-sided than often imagined. 'Exotheology' is a lively subdiscipline within several religious traditions. This Element offers a wide-ranging introduction to the multifarious 'problems of God and astrobiology', real and perceived. It covers major topics within Christian theology (e.g., creation, incarnation, salvation), as well as issues specific to Judaism, Islam, Buddhism, and Hinduism. It also discusses the very different perspectives offered by other (non)religious traditions, including Mormonism, various 'alien-positive' new religious movements (e.g., Heaven's Gate, Scientology, Raelism), and the 'Ancient Astronaunt' theories popularized by Erich von Daniken and the History channel's Ancient Aliens.